Korean J. Math. Vol. 27 No. 2 (2019) pp.445-463
DOI: https://doi.org/10.11568/kjm.2019.27.2.445

A Banach algebra of series of functions over paths

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Published: Jun 30, 2019
Keywords:
Analytic Wiener integral, analytic Feynman integral, Banach algebra, It\^o integral, Paley-Wiener-Zygmund integral, Wiener space
Mathematics Subject Classification:
46J10, 28C20, 60H05.

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Dong Hyun Cho
Department of Mathematics, Kyonggi University, Republic of Korea
Mo A Kwon
Department of Mathematics, Kyonggi University, Republic of Korea

Abstract

Let $C[0,T]$ denote the space of continuous real-valued functions on $[0,T]$. On the space $C[0,T]$, we introduce a Banach algebra of series of functions which are generalized Fourier-Stieltjes transforms of measures of finite variation on the product of simplex and Euclidean space. We evaluate analytic Feynman integrals of the functions in the Banach algebra which play significant roles in the Feynman integration theory and quantum mechanics.


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Supporting Agencies

the National Research Foundation (NRF) of Korea

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